Geometry Unit 10

Big Idea:

Identify and use the properties of circles to solve problems. Write the equation of a circle and graph.

Student Expectations:

Priority TEKS

G.12(A) [Supporting] apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems

Focus TEKS

G.5(A) [Readiness] investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

G.12(E) [Supporting] show that the equation of a circle with center at the origin and radius r is x²+ y²= r² and determine the equation for the graph of a circle with radius r and center (h, k), (x – h)² + (y – k)² = r²

Ongoing TEKS

G.5(A) [Readiness] investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

Student Learning Targets:

• I will find the center and radius of a circle given its equation.
• I will write the equation of a circle in the form (x - h)² + (y - k)² = r² by completing the square.
• I will solve problems using:
  • Arcs
  • Chords
  • Diameters of circles
  • Tangent segments
  • Inscribed angles
  • Angles formed by chords
  • Relationships among arcs and central angles
  • Angles formed by tangents or secants
• I will describe relationships among:
  • Tangents and radii of a circle
  • Diameters and chords of a circle
  • Inscribed angles, central angles, and arcs
  • Angles formed by intersecting chords in a circle
  • The angles formed by tangents to a circle of secants to a circle.
• I will prove and apply theorems about chords of a circle.
• I will prove that tangent segments to a circle from a point outside the circle are congruent.
• I will understand how to measure an arc of a circle.

Essential Questions:

• Why is it important to understand coordinate geometry and geometric constructions?
• How can properties of circles and their intersecting lines be used to verify properties of other geometric figures?

Extra Information:

Adopted Textbook: Springboard - Geometry Texas Edition

District Grading Policy

Texas Gateway Online Resource Center